2 problems

Let $[n]=\{1,\ldots,n\}$, let $\mathcal G$ be a hypergraph over the ground set $[n]$, and let $r\geq s\geq 2$. Write $\mathcal G_{\widetilde{\{s\text{-stable}\}}}$ for the correspo…

Let $r\geq 3$, let $[n]=\{1,\ldots,n\}$, and let $\mathcal G$ be a hypergraph over the ground set $[n]$. Write $\mathcal G_{r\text{-stable}}$ for the hypergraph obtained by restric…